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A linear dependency among vectors v(1) to v(k) is an equation, in which some of the c’s ar not 0. A set of vectors is said to be linearly independent if there is no linear dependence among them, and linearly dependent if there is one or more linear dependence.

Example: Suppose v(1) = i + j; v(2) =2i; v(3) = 3j.

Then v(1), v(2) and v(3) are linearly dependent:
6v(1) = 3v(2) + 2v(3), or 6v(1) - 3v(2) - 2v(3) = 0

Exercise 3.11 Prove: any k + 1  k-vectors are linearly dependent. (you can do it by using mathematical induction.) (if you are not familiar with mathematical induction read this solution and become familiar with it!) Solution